Abstract A community structure in a complex network often exhibits hierarchical characteristics. Current hierarchical community‐discovery algorithms generally consider a single node as a community during the initial stage. This approach leads to over‐fine clustering granularity, too‐deep clustering levels, and other issues. Therefore, this article proposes a hierarchical community‐discovery algorithm that combines the core nodes and the three‐order structure model. Between neighboring nodes, there is a first‐order structure. The core node is identified based on its influence, and the similarity between the core node and its neighboring nodes is defined as the second‐order structure. The nodes satisfying the second‐order structure are then formed into a friend circle. The similarity between friend circles is defined as the third‐order structure. According to this structure, the friend circles are construed as a hierarchical clustering tree (HCT) where one HCT represents a community. The HCT built by this algorithm has relatively fewer levels and exhibits a flat feature. Experimental results on both artificial and real networks show that the algorithm performs well on various indicators. Additionally, the algorithm exhibits near‐linear time complexity.

Abstract While contemporary community‐based recommendation algorithms based on a single community structure are more capable of processing large datasets than ever, they lack recommendation precision. This article proposes a collaborative filtering recommendation algorithm that integrates community structure and user implicit trust. The algorithm first applies a method based on the Gaussian function to fill the matrix of item ratings of users to alleviate data sparsity. It then uses the trust matrix to obtain the asymmetric trust relationship of the trustor and trustee, based on which the degree of users' implicit trust is calculated. The users are divided into communities based on the implicit trust degree to determine the influence among users more accurately. The algorithm then predicts the target user's rating using the ratings of users in the community to generate recommendations. To verify the performance of the proposed algorithm, we compared the proposed algorithm with three contemporary algorithms under the same conditions using FilmTrust datasets. The recommendation accuracy as well as the mean absolute error and root mean square error values of the proposed algorithm were better than those of the other four algorithms by approximately 14% and 4%, respectively. The experimental results demonstrate that the proposed algorithm can achieve better recommendation efficiency than existing algorithms.

Abstract Community detection on high‐mixed networks has been a challenging problem for complex network researchers. In a Lancichinetti–Fortunato–Radicchi (LFR) network with a mixing parameter mu greater than or equal to 0.5, the quality of the communities partitioned by currently available algorithms will decrease rapidly with increasing mu. To address this issue, we propose a label propagation algorithm on high‐mixed networks, called LPA‐HM, for community detection. In our algorithm, the initial node labels are preprocessed using the number of common neighbors of the nodes, which greatly reduces the initial number of labels and thus improves the quality of the subsequent label propagation process. During the label propagation stage, each node is given the label that is shared by the maximum number of its neighbors. If there are several labels that meet this requirement, the influence of the labels' nodes is calculated, and the label with the maximum total influence is selected as the label of the current node. Early stop conditions based on modularity and run‐to‐run changes in the number of detected communities are incorporated in the algorithm to prevent label overpropagation. The communities that fail to satisfy the definition of weak communities are merged with their most similar neighboring communities. In experiments based on real networks and LFR networks, it is found that the LPA‐HM algorithm is well suited to community detection in a variety of networks. In a high‐mixed LFR network with mu = 0.7, the NMI measure of the LPA‐HM algorithm's community detection performance is still greater than 0.9.

We propose an overlapping community discovery algorithm that combines node influence and [Formula: see text]-connected neighbors for effectively detecting the overlapping community structure of complex networks. On the basis of the node influence and [Formula: see text]-connected neighbors, our method accurately detects the core node community and uses the improved similarity between the node and community to expand the core node community. Accordingly, the discovery and optimization of network overlapping communities are realized. Experiments on artificial and real-world networks demonstrate that our method significantly and consistently outperforms other comparison methods.